Algorithmic Consistency in Computational Inelasticity – a Conceptual Completion

Abstract

AbstractThis paper communicates a new algorithmic concept, how higher‐order Runge‐Kutta (RK) methods for time integration of viscoelastic constitutive laws can be introduced into nonlinear finite element methods in order (i) to obtain the full nominal order p in time integration, (ii) to ensure that global equilibrium is only required at the end of time intervals Δt but not in the interior at RK‐stages, and (iii) to obtain –based on (i) and (ii)– a considerable speed‐up compared with Backward‐Euler. The condition to realize (i)–(iii) is, that the approximation of total strain in time must be of the same order as the time‐integration method, which is a completion of the concept of algorithmic consistency in computational inelasticity. (© 2013 Wiley‐VCH Verlag GmbH & Co. KGaA, Weinheim)